Calculus: Early Transcendentals, Chapter 4, 4.1, Section 4.1, Problem 51

Given: f(x)=3x^4-4x^3-12x^2+1,[-2,3].
Find the critical numbers by setting the first derivative equal to zero and solving for the x value(s).
f'(x)=12x^3-12x^2-24x=0
12x(x^2-x-2)=0
12x(x-2)(x+1)=0
x=0,x=2,x=-1
The critical numbers are x=0,x=2, and x=-1. Plug in the critical numbers and the endpoints of the interval [-2,3] into the original f(x) function.
f(-2)=33
f(-1)=-4
f(0)=1
f(2)=-31
f(3)=28
Examine the f(x) values to determine the absolute maximum and absolute minimum.
The absolute maximum value occurs at the point (-2, 33).
The absolute minimum value occurs at the point (2, -31).